During the 1995–96 season, English club Sheffield Wednesday signed Stefanović and his compatriot, striker Darko Kovačević. Stefanović cost the English club £2 million. However, Stefanović struggled to break into the Wednesday side with Emerson Thome and Des Walker among those ahead of him in the pecking order.

In 1998–99, after playing 72 games for the club, Stefanović was released on a free transfer after he failed to make enough first-team appearances to qualify for a work permit extension.

Stefanović moved to his third club of the 1999–2000 season when transferring to Vitesse Arnhem of the Netherlands. He quickly became a first team regular, and spent four years at the club, becoming captain during that time. At Vitesse he played six UEFA Cup matches.

At the start of the 2003–04 season, Stefanović returned to England with Premiership newcomers Portsmouth for £1.85 million.[3] He established himself as a first-choice defender during the club's first season in the top-flight, and was a regular in the 2004–05 campaign, winning the fans' Player of the season award.[4] He was made Portsmouth captain by Alain Perrin in the 2005–06 season, although a dip in form and a habit of speaking out to the press earned him the ire of some supporters. Indeed, he confessed to "not giving 100%" under Perrin due to disliking the French coach, comments criticised as highly unprofessional by some fans.

Stefanović's influence on chairman (and fellow Serbian) Milan Mandarić is said to have been an important factor in the dismissal of Perrin and the re-appointment of Harry Redknapp, and he was an important member of the side that ensured Premiership survival at Wigan in the penultimate game of the season.

Stefanović was converted to a left-back at the start of 2006–07 and was a mainstay of the defence that performed so well for Portsmouth during the season. However, the arrivals of Hermann Hreiðarsson and Sylvain Distin during the summer of 2007 cast his position as a first team regular into doubt and he was replaced as captain by Sol Campbell for the 2007–08 season.

Having spent less than a year at Craven Cottage, Stefanović dropped down a division to join Norwich City on 18 July 2008, agreeing a two-year deal.[7]
After twelve starts for the Canaries, during which he picked up one red card, Stefanović ruptured his cruciate knee ligaments and didn't play again for Norwich City in the 2008–09 season.

In August 2009, it was reported that Stefanović was in negotiations to leave Norwich, with the player wishing to return to the south of England.[8] On 1 September 2009, his contract was terminated by mutual consent.[9]

Stefanović is a full Serbian international, earning his first call-up in 1995 (the country was then known as Yugoslavia, changing to Serbia and Montenegro in 2003). He has a total of 20 caps to his name. Stefanović retired from international football in 2004.